The 400 Series cameras (D415 and D435) work with any Intel or ARM processor and just need a USB 3.0 port. So since Odroid has an ARM processor and 2 USB 3.0 ports, it should be fine with the D435.
http://www.hardkernel.com/main/products/prdt_info.php ODROID | Hardkernel
In regard to Ubuntu MATE: it is the first time I have heard of this OS. I would speculate that the generic version of Ubuntu MATE would have the best chance of working, rather than the one optimized for Raspberry Pi.
https://ubuntu-mate.org/armhf-rootfs/ Ubuntu MATE generic armhf rootfs | Ubuntu MATE
This OS requires ARMv7 architecture, which the Odroid XU4's ARM Cortex-A15 apparently has.
https://en.wikipedia.org/wiki/ARM_Cortex-A15 ARM Cortex-A15 - Wikipedia
It is important to note that the RealSense SDK 2.0 software recommends Ubuntu 14 / 16.04 LTS. So I culd not give a guarantee that it would work with Ubuntu MATE.
